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Angle of incidence of sun rays Calculator

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✖The Latitude Angle is the angular measurement that indicates a location's distance north or south of the equator, influencing solar energy exposure and system performance.ⓘ Latitude Angle [Φ]			+10% -10%
✖The Declination Angle is the angle between the rays of the sun and the plane of the Earth's equator, affecting solar energy collection throughout the year.ⓘ Declination Angle [δ]			+10% -10%
✖The Tilt Angle is the angle at which solar panels are positioned relative to the ground, optimizing sunlight exposure for increased energy efficiency.ⓘ Tilt Angle [β]			+10% -10%
✖The Surface Azimuth Angle is the angle between the north direction and the projection of a surface's normal onto the horizontal plane, important for solar energy applications.ⓘ Surface Azimuth Angle [γ]			+10% -10%
✖The Hour angle is the measure of time since solar noon, expressed in degrees, indicating the position of the sun in the sky relative to an observer.ⓘ Hour angle [ω]			+10% -10%

✖The Angle Of Incidence is the angle between incoming solar radiation and a surface, influencing the amount of solar energy absorbed by that surface.ⓘ Angle of incidence of sun rays [θ]

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Angle of incidence of sun rays Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle Of Incidence = acos(sin(Latitude Angle)*(sin(Declination Angle)*cos(Tilt Angle)+cos(Declination Angle)*cos(Surface Azimuth Angle)*cos(Hour angle)*sin(Tilt Angle))+cos(Latitude Angle)*(cos(Declination Angle)*cos(Hour angle)*cos(Tilt Angle)-sin(Declination Angle)*cos(Surface Azimuth Angle)*sin(Tilt Angle))+cos(Declination Angle)*sin(Surface Azimuth Angle)*sin(Hour angle)*sin(Tilt Angle))
θ = acos(sin(Φ)*(sin(δ)*cos(β)+cos(δ)*cos(γ)*cos(ω)*sin(β))+cos(Φ)*(cos(δ)*cos(ω)*cos(β)-sin(δ)*cos(γ)*sin(β))+cos(δ)*sin(γ)*sin(ω)*sin(β))
This formula uses 3 Functions, 6 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)

Variables Used

Angle Of Incidence - (Measured in Radian) - The Angle Of Incidence is the angle between incoming solar radiation and a surface, influencing the amount of solar energy absorbed by that surface.
Latitude Angle - (Measured in Radian) - The Latitude Angle is the angular measurement that indicates a location's distance north or south of the equator, influencing solar energy exposure and system performance.
Declination Angle - (Measured in Radian) - The Declination Angle is the angle between the rays of the sun and the plane of the Earth's equator, affecting solar energy collection throughout the year.
Tilt Angle - (Measured in Radian) - The Tilt Angle is the angle at which solar panels are positioned relative to the ground, optimizing sunlight exposure for increased energy efficiency.
Surface Azimuth Angle - (Measured in Radian) - The Surface Azimuth Angle is the angle between the north direction and the projection of a surface's normal onto the horizontal plane, important for solar energy applications.
Hour angle - (Measured in Radian) - The Hour angle is the measure of time since solar noon, expressed in degrees, indicating the position of the sun in the sky relative to an observer.

STEP 1: Convert Input(s) to Base Unit

Latitude Angle: 55 Degree --> 0.959931088596701 Radian (Check conversion here)
Declination Angle: 23.09638 Degree --> 0.403107876291692 Radian (Check conversion here)
Tilt Angle: 5.5 Degree --> 0.0959931088596701 Radian (Check conversion here)
Surface Azimuth Angle: 0.25 Degree --> 0.004363323129985 Radian (Check conversion here)
Hour angle: 119.8015 Degree --> 2.09093062382759 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = acos(sin(Φ)*(sin(δ)*cos(β)+cos(δ)*cos(γ)*cos(ω)*sin(β))+cos(Φ)*(cos(δ)*cos(ω)*cos(β)-sin(δ)*cos(γ)*sin(β))+cos(δ)*sin(γ)*sin(ω)*sin(β)) --> acos(sin(0.959931088596701)*(sin(0.403107876291692)*cos(0.0959931088596701)+cos(0.403107876291692)*cos(0.004363323129985)*cos(2.09093062382759)*sin(0.0959931088596701))+cos(0.959931088596701)*(cos(0.403107876291692)*cos(2.09093062382759)*cos(0.0959931088596701)-sin(0.403107876291692)*cos(0.004363323129985)*sin(0.0959931088596701))+cos(0.403107876291692)*sin(0.004363323129985)*sin(2.09093062382759)*sin(0.0959931088596701))

Evaluating ... ...

θ = 1.56907270195998

STEP 3: Convert Result to Output's Unit

1.56907270195998 Radian -->89.9012435715125 Degree (Check conversion here)

FINAL ANSWER

89.9012435715125 ≈ 89.90124 Degree <-- Angle Of Incidence

(Calculation completed in 00.004 seconds)

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DIT UNIVERSITY (DITU), Dehradun

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< Basics Calculators

Hour Angle at Sunrise and Sunset

LaTeX Go Hour angle = acos(-tan(Latitude Angle-Tilt Angle)*tan(Declination Angle))

Tilt factor for reflected radiation

LaTeX Go Tilt factor for reflected radiation = (Reflectivity*(1-cos(Tilt Angle)))/2

Tilt factor for diffused radiation

LaTeX Go Tilt factor for diffused radiation = (1+cos(Tilt Angle))/2

Hour angle

LaTeX Go Hour angle = (Solar Time/3600-12)*15*0.0175

Angle of incidence of sun rays Formula

LaTeX Go

What is Angle of Incidence of Sun Rays?

The angle of incidence of sun rays is the angle at which sunlight strikes the Earth's surface. It varies depending on the time of day, latitude, and season, influencing the intensity and distribution of solar energy. A higher angle (closer to 90 degrees) results in more direct sunlight and greater heating, while a lower angle spreads the sunlight over a larger area, reducing its intensity. This angle plays a key role in climate patterns, solar panel efficiency, and daylight duration.

How to Calculate Angle of incidence of sun rays?

Angle of incidence of sun rays calculator uses Angle Of Incidence = acos(sin(Latitude Angle)*(sin(Declination Angle)*cos(Tilt Angle)+cos(Declination Angle)*cos(Surface Azimuth Angle)*cos(Hour angle)*sin(Tilt Angle))+cos(Latitude Angle)*(cos(Declination Angle)*cos(Hour angle)*cos(Tilt Angle)-sin(Declination Angle)*cos(Surface Azimuth Angle)*sin(Tilt Angle))+cos(Declination Angle)*sin(Surface Azimuth Angle)*sin(Hour angle)*sin(Tilt Angle)) to calculate the Angle Of Incidence, The Angle of Incidence Of Sun Rays formula is defined as the angle formed between the direction of the sun ray and the line normal to the surface. Angle Of Incidence is denoted by θ symbol.

How to calculate Angle of incidence of sun rays using this online calculator? To use this online calculator for Angle of incidence of sun rays, enter Latitude Angle (Φ), Declination Angle (δ), Tilt Angle (β), Surface Azimuth Angle (γ) & Hour angle (ω) and hit the calculate button. Here is how the Angle of incidence of sun rays calculation can be explained with given input values -> 5150.962 = acos(sin(0.959931088596701)*(sin(0.403107876291692)*cos(0.0959931088596701)+cos(0.403107876291692)*cos(0.004363323129985)*cos(2.09093062382759)*sin(0.0959931088596701))+cos(0.959931088596701)*(cos(0.403107876291692)*cos(2.09093062382759)*cos(0.0959931088596701)-sin(0.403107876291692)*cos(0.004363323129985)*sin(0.0959931088596701))+cos(0.403107876291692)*sin(0.004363323129985)*sin(2.09093062382759)*sin(0.0959931088596701)).

FAQ

What is Angle of incidence of sun rays?

The Angle of Incidence Of Sun Rays formula is defined as the angle formed between the direction of the sun ray and the line normal to the surface and is represented as θ = acos(sin(Φ)*(sin(δ)*cos(β)+cos(δ)*cos(γ)*cos(ω)*sin(β))+cos(Φ)*(cos(δ)*cos(ω)*cos(β)-sin(δ)*cos(γ)*sin(β))+cos(δ)*sin(γ)*sin(ω)*sin(β)) or Angle Of Incidence = acos(sin(Latitude Angle)*(sin(Declination Angle)*cos(Tilt Angle)+cos(Declination Angle)*cos(Surface Azimuth Angle)*cos(Hour angle)*sin(Tilt Angle))+cos(Latitude Angle)*(cos(Declination Angle)*cos(Hour angle)*cos(Tilt Angle)-sin(Declination Angle)*cos(Surface Azimuth Angle)*sin(Tilt Angle))+cos(Declination Angle)*sin(Surface Azimuth Angle)*sin(Hour angle)*sin(Tilt Angle)). The Latitude Angle is the angular measurement that indicates a location's distance north or south of the equator, influencing solar energy exposure and system performance, The Declination Angle is the angle between the rays of the sun and the plane of the Earth's equator, affecting solar energy collection throughout the year, The Tilt Angle is the angle at which solar panels are positioned relative to the ground, optimizing sunlight exposure for increased energy efficiency, The Surface Azimuth Angle is the angle between the north direction and the projection of a surface's normal onto the horizontal plane, important for solar energy applications & The Hour angle is the measure of time since solar noon, expressed in degrees, indicating the position of the sun in the sky relative to an observer.

How to calculate Angle of incidence of sun rays?

The Angle of Incidence Of Sun Rays formula is defined as the angle formed between the direction of the sun ray and the line normal to the surface is calculated using Angle Of Incidence = acos(sin(Latitude Angle)*(sin(Declination Angle)*cos(Tilt Angle)+cos(Declination Angle)*cos(Surface Azimuth Angle)*cos(Hour angle)*sin(Tilt Angle))+cos(Latitude Angle)*(cos(Declination Angle)*cos(Hour angle)*cos(Tilt Angle)-sin(Declination Angle)*cos(Surface Azimuth Angle)*sin(Tilt Angle))+cos(Declination Angle)*sin(Surface Azimuth Angle)*sin(Hour angle)*sin(Tilt Angle)). To calculate Angle of incidence of sun rays, you need Latitude Angle (Φ), Declination Angle (δ), Tilt Angle (β), Surface Azimuth Angle (γ) & Hour angle (ω). With our tool, you need to enter the respective value for Latitude Angle, Declination Angle, Tilt Angle, Surface Azimuth Angle & Hour angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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